U.S. Department of the Interior

U.S. Geological Survey

The National Flood-Frequency Program—Methods for Estimating Flood 

Magnitude and Frequency in Rural Areas in Maryland, 2001

Introduction

Estimates of the magnitude and frequency of flood-peak discharges and flood 

hydrographs are used for a variety of purposes, such as for the design of bridges, 

culverts, and flood-control structures; and 

for the management and regulation of 

flood plains. To provide simple methods of 

estimating flood-peak discharges, the U.S. 

Geological Survey (USGS) has developed 

and published regression equations for 

every State, the Commonwealth of Puerto 

Rico, American Samoa, and a number of 

metropolitan areas in the United States. In 

1993, the USGS, in cooperation with the 

Federal Emergency Management Agency 

and the Federal Highway Administration, 

compiled all current USGS statewide and 

metropolitan area regression equations into 

a computer program titled “The National 

Flood-Frequency (NFF) Program” 

(Jennings and others, 1994). 

Since 1993, new or updated regression equations have been developed by the 

USGS for various areas of the Nation. 

These new equations have been incorporated into an updated version of the NFF 

Program. 

This fact sheet describes the application of the updated NFF Program to 

streams that drain rural areas in Maryland. 

Information on obtaining the NFF software 

and fact sheets for other areas of the 

Nation is provided at the end of this Fact 

Sheet.

Overview

Dillow (1996) developed regression 

equations for estimating peak discharges 

(QT), in cubic feet per second, that have 

recurrence intervals (T) that range from 2 

to 500 years for unregulated, rural, nontidal Maryland streams. Separate equations 

were developed for each of the five physiographic provinces in Maryland: Appalachian Plateaus, Blue Ridge and Valley and 

Ridge, Piedmont, Western Coastal Plain, 

and Eastern Coastal Plain (fig. 1). Analysis 

of regression residuals was used to confirm 

the validity of subdividing the State on the 

basis of physiographic provinces.

The regression equations were developed using peak-discharge data through 

September 30, 1990, from streamflowgaging stations at 107 locations in Maryland and 112 locations in Delaware, Pennsylvania, Virginia, and West Virginia. 

Dillow (1996) presented the peak-flow 

data and explanatory watershed variables 

for the 219 streamflow-gaging stations 

used to develop the regression equations.

Procedure

The equations are based on the inchpound system of units, but the NFF Program will accept and report either the inchpound or the metric system of units. The 

explanatory watershed variables used in 

the regression equations are as follow:

Drainage area (A), in square miles, is the 

total area that contributes runoff upstream 

of the stream site of interest determined by 

planimeter from the best available topographic maps.

Storage (ST) is the percentage of drainage 

area, A, that is covered by lakes and ponds 

determined by planimeter from USGS 

topographic maps of areas of blue overprint. The constant of 10 is added to ST by 

the NFF Program; the user enters the 

actual value of ST.

40°

38°

79° 76°

BASE FROM U.S. GEOLOGICAL SURVEY, 1:500,000

Figure 1. Study area and physiographic provinces in Maryland.

0

0

30 MILES

30 KILOMETERS

WEST VIRGINIA VIRGINIA

 NEW

JERSEY

DELAWARE

Washington, D.C.

A T L A N T I C

 O C E A N 

D E L A W A R E

B A Y

POTOMAC

POTOMAC

RIVER

RIVER

APPALACHIAN

PLATEAUS

BLUE RIDGE

PIEDMONT

VALLEY

AND RIDGE

EASTERN

COASTAL PLAIN 

WESTERN

COASTAL PLAIN 

C

H

E

S

A

P

E

A

K

E

B

A

Y

PENNSYLVANIA

MARYLAND

FALL

LINE

USGS Fact Sheet 098-01

December, 2001
Limestone geology (LI) is the percentage 

of drainage area, A, that is underlain by 

limestone or dolomite determined by 

planimeter from geologic maps by 

Edwards (1978) and Berg (1980). The constant 10 is added to LI by the NFF Program; the user enters the actual value of LI.

Runoff-curve number (RCN) represents 

the effect of hydrologic soil type and land 

use (U.S. Department of Agriculture, 

1985). Hydrologic soil type coverage can 

be determined from Maryland Department 

of State Planning (1973) natural soil 

groups maps. When more than one hydrologic soil type or land use is present in a 

basin, a weighted RCN should be determined based on the percentage of drainage 

each hydrologic soil-type / land-use combination contributes to the entire drainage 

area. The constant 33 is subtracted from 

RCN by the NFF Program; the user enters 

the actual value of RCN.

Area of forest (F) is the percentage of 

drainage area, A, that is covered by forests 

determined by planimeter from USGS 

topographic maps of areas of green overprint. The constant 10 is added to F by the 

NFF Program; the user enters the actual 

value of F.

Basin relief (BR), in feet (National Geodetic Vertical Datum of 1929), is the difference in elevation between the mean basin 

elevation, as determined from topographic 

maps by the grid-sampling method, and 

the basin outlet.

The regression equations, the average 

standard errors of prediction, and the 

equivalent years of record are shown in 

table 2. The average standard error of prediction is a measure of the accuracy of a 

regression equation when used to estimate 

peak discharges for ungaged watersheds 

similar to those used to derive the regression equation. Errors in the QT estimates 

for about two-thirds of the ungaged sites 

will be within the given standard errors. 

Errors increase appreciably when any of 

the basin characteristics used in the equations are near or beyond the range limits 

shown in table 3. The equivalent years of 

record is the number of years of streamflow record needed to achieve the same 

accuracy as the regression equation.

Improving Estimates With 

Gaged Data

Dillow (1996) developed weighting 

techniques to improve estimates of peak 

discharge at gaged locations by combining 

the estimates derived from analysis of gage 

records with estimates derived from the 

regression equations. The weights of these 

two independent estimates are based on the 

length of the gage record (in years) and the 

equivalent years of record of the applicable 

regression equation. The weighted estimate of peak discharge is computed as

where

QT(G)w is the weighted estimate of discharge Q for recurrence interval 

T at the gage location,

QT(G)s is the estimate of QT derived 

from analysis of the systematic 

gage records,

QT(G)r is the estimate of QT derived 

from application of the appropriate regression equation in 

table 2,

N is the number of years in the 

gage record used to compute 

QT(G)s, and

EQ is the equivalent years of record 

(table 2).

The accuracy of the weighted discharge 

estimate, in equivalent years of record, is 

equal to N + EQ. The NFF Program performs these computations. 

QT( ) G w log

N QT G( )s ⋅log EQ QT( ) G r + ⋅log

N EQ + = --------------------------------------------------------------------------

Table 1. Runoff-curve numbers defined by land use and hydrologic soil type in Maryland 

(from Dillow, 1996)

[Hydrologic soil types: A, soil with low runoff potential; B, soil with moderately low runoff potential; C, soil 

with moderately high runoff potential; and D, soil with high runoff potential; DU/AC, dwelling units per acre; 

>, greater than]

Hydrologic soil type

Land-use category A B C D

Residential (0.2 to 2 DU/AC) 54 70 80 85

Residential (>2 to 8 DU/AC) 61 75 83 87

Residential (>8 DU/AC) 77 85 90 92

Commercial/Industrial 89 92 94 95

Institutional 81 88 91 93

Forest 36 60 73 9

Brush 35 56 70 77

Water 100 100 100 100

Wetlands 100 100 100 100

Beach/barren/extractive 77 86 91 94

Cropland 72 81 88 91

Grass 49 69 79 84
Ungaged Sites Near Gaged 

Sites on the Same Stream

Dillow (1996) showed how the 

weighted estimate of peak discharge for a 

gaged site can be used to improve estimates of peak discharge for an ungaged 

site on the same stream with a drainage 

area that is between 50 and 150 percent of 

the drainage area for the gaged site. The 

regression estimate for the ungaged site is 

multiplied by an adjustment factor, which 

is computed as

,

where

AF is the adjustment factor,

∆A is the absolute value of the difference in drainage area between 

AF R ∆A R( ) – 1

0.5AG

= – -------------------------

Table 2. Flood-peak discharge regression equations and associated statistics for streams

that drain rural areas in Maryland (modified from Dillow, 1996)

[QT, peak discharge for recurrence interval T, 2 to 500 years, in cubic meters per second; A, drainage area, in

square miles; F, forest cover, in percent; BR, basin relief, in feet; LI, limestone geology (limestone, dolomite), in

percent; RCN, runoff-curve number; ST, storage (lakes, ponds, and swamps), in percent]

Average

standard

error of Equivalent

prediction, years of

Regression equations in percent record

Appalachian Plateaus Province (46 gaging stations)

Q2 = 106A0.851(F+10)-0.223BR0.056 24 5

Q5 = 109A0.858(F+10)-0.143BR0.064 22 10

Q10 = 113A0.859(F+10)-0.106BR0.072 21 14

Q25 = 118A0.858(F+10)-0.072BR0.087 23 18

Q50 = 121A0.858(F+10)-0.051BR0.099 25 20

Q100 = 124A0.858(F+10)-0.033BR0.111 28 20

Q500 = 127A0.859(F+10)0.004BR0.140 35 19

Blue Ridge and Valley and Ridge Province (34 gaging stations)

Q2 = 4,260A0.774(LI+10)-0.549BR-0.405 50 2

Q5 = 6,670A0.752(LI+10)-0.564BR-0.354 45 4

Q10 = 8,740A0.741(LI+10)-0.579BR-0.326 42 7

Q25 = 12,000A0.730(LI+10)-0.602BR-0.295 41 12

Q50 = 15,100A0.723(LI+10)-0.620BR-0.276 40 15

Q100 = 18,900A0.719(LI+10)-0.639BR-0.261 41 18

Q500 = 31,800A0.712(LI+10)-0.686BR-0.241 45 23

Piedmont Province (81 gaging stations)

Q2 = 451A0.635(F+10)-0.266 39 3

Q5 = 839A0.606(F+10)-0.248 36 7

Q10 = 1,210A0.589(F+10)-0.242 35 10

Q25 = 1,820A0.574(F+10)-0.239 37 15

Q50 = 2,390A0.565(F+10)-0.240 40 17

Q100 = 3,060A0.557(F+10)-0.241 43 19

Q500 = 5,190A0.543(F+10)-0.245 52 20

Western Coastal Plain Province (21 gaging stations)

Q2 = 1,4100.761(F+10)-0.782 55 2

Q5 = 1,780A0.769(F+10)-0.687 51 4

Q10 = 1,910A0.771(F+10)-0.613 51 7

Q25 = 2,000A0.772(F+10)-0.519 54 10

Q50 = 2,060A0.771(F+10)-0.452 58 12

Q100 = 2,140A0.770(F+10)-0.391 63 13

Q500 = 2,380A0.765(F+10)-0.263 77 14

Eastern Coastal Plain Province (37 gaging stations)

Q2 = 0.25A0.591(RCN-33)1.70BR0.310(F+10)-0.464(ST+10)-0.148 46 2

Q5 = 1.05A0.595(RCN-33)1.74BR0.404(F+10)-0.586(ST+10)-0.498 46 5

Q10 = 3.24A0.597(RCN-33)1.71BR0.436(F+10)-0.667(ST+10)-0.694 45 7

Q25 = 13.1A0.597(RCN-33)1.66BR0.457(F+10)-0.770(ST+10)-0.892 45 12

Q50 = 35.0A0.594(RCN-33)1.62BR0.465(F+10)-0.847(ST+10)-1.01 45 16

Q100 = 87.6A0.589(RCN-33)1.58BR0.470(F+10)-0.923(ST+10)-1.11 46 19

Q500 = 627A0.573(RCN-33)1.49BR0.478(F+10)-1.10(ST+10)-1.29 48 28
the gaged site (AG) and the 

ungaged site (AU), |AG-AU|, and

R is the ratio of the weighted peakdischarge estimate at the gaged 

site to the regression estimate at 

the ungaged site, 

QT(G)w/QT(G)r).

The equations are used without adjustment 

where the drainage area of the ungaged site 

is not within 50 to 150 percent the drainage 

area of the gaged site.

Sites in Transition Zones

When the drainage area of the site of 

interest is in more than one physiographic 

province, a weighted estimate of the peak 

discharge should be computed. The equations for the appropriate regions should be 

applied independently using basinwide 

estimates of the required explanatory variable. The weighted estimate is then computed by multiplying each regional 

estimate against the fraction of the drainage area in that region and summing the 

products. The NFF Program performs this 

computation.

—Prepared by Robert R. Mason, Jr. and 

Luis A. Fuste of the U.S. Geological Survey; and Jeffrey N. King and Wilbert O. 

Thomas, Jr., of Michael Baker, Jr., Inc.

References

Berg, T.M., comp., 1980, Geologic map of 

Pennsylvania: Pennsylvania Topographic and Geologic Survey, 4th 

Series, 1 map on 2 sheets, scale 

1:250,000 plus 1 sheet of cross sections.

Dillow, J.J.A., 1996, Technique for estimating magnitude and frequency of 

peak flows in Maryland: U.S. Geological Survey Water-Resources 

Investigations Report 95–4154, 55 p.

Edwards, J.E., Jr., comp., 1978, Geologic 

map of Washington County: Maryland Geological Survey, 1 sheet, scale 

1:62,500.

Jennings, M.E., Thomas, W.O., Jr., and 

Riggs, H.C., comps., 1994, Nationwide summary of U.S. Geological 

Survey regional regression equations 

for estimating magnitude and frequency of floods for ungaged sites, 

1993: U.S. Geological Survey WaterResources Investigations Report 

94–4002, 196 p.

Maryland Department of State Planning, 

1973, Natural soil groups report: 

Maryland Department of State Planning Report No. 199, 153 p.

U.S. Department of Agriculture, 1985, Soil 

Conservation Service National Engineering Handbook, Section 4, 

Hydrology.

For more information contact:

U.S. Geological Survey

Office of Surface Water

415 National Center

Reston, Virginia 20192

(703) 648-5301

USGS hydrologic analysis software is 

available for electronic retrieval through 

the World Wide Web (WWW) at 

http://water.usgs.gov/software/ 

and through anonymous File Transfer Protocol (FTP) from water.usgs.gov 

(directory: /pub/software). The WWW 

page and anonymous FTP directory from 

which the National Flood-Frequency software and user documentation can be 

retrieved are 

http://water.usgs.gov/software/nff.html 

and 

/pub/software/surface_water/nff, 

respectively.

Additional earth science information is 

available from the USGS through the 

WWW at http://www.usgs.gov/ 

or by calling 1-888-ASK-USGS.

Table 3. Range of explanatory variables for which regression equations are applicable for streams that drain rural areas in Maryland

(from Dillow, 1996)

[--, data either not applicable or not significant]

Carbonate

Drainage area, rock coverage, Storage, Basin relief, Forest cover, Runoff-curve

Physiographic province in square miles in percent in percent in feet in percent number

Appalachian Plateaus 0.22–247 -- -- 88–1,431 28–96 --

Blue Ridge and Valley and Ridge .10–494 0–100 -- 18–745 -- --

Piedmont .26–165 -- -- -- 0–96 --

Western Coastal Plain .30–54.8 -- -- -- 19–83 --

Eastern Coastal Plain 3.80–113 -- 0.000–15.8 4–57 8–85 72.85–87.29